Include a Javascript variable in the MongoDB aggregate query with $project

I have a javascript loop that does a particular task of looping over a javascript hash and calling aggregate over my collection.

I was able to insert a variable into the aggregate query for the $match function, but I cannot for the $project function.

I want to match across the hash keys and then display the hash values in conjunction with the values already in the document that I just matched. These hash values and label were not in the document beforehand.

var cmtss = {};

for (var item in cursor['result'])
{
    var prov = cursor['result'][item]['prov_group'];
    cmtss[cursor['result'][item]['name']] = prov;
}

for (var item in cmtss)
{
    var cmts = "$" + cmtss[item];

    result = db.modems.aggregate( { $match : { cmts: item } } ,
                                  { $project : {
                                       ip : "$ip",
                                       model : "$model",
                                       cmts : "$cmts",
                                       prov_group : cmts } } );
    printjson(result);
}

As you can see, I include a $match, where I want the cmts field to match to the key provided. But with those matches I want to display the 3 fields including a brand new field that I add in but its value is the hash value from cmtss. I tried with and without the $ operator before the value. It is simply not displaying a prov_group at all in the result documents.

Do I need to use $add somehow?